Question: How many numbers between $1$ and $100$ (inclusive) are divisible by $3$ or $2$ ?
Explanation: There are $33$ numbers divisible by $3$ between $1$ and $100$, and $50$ numbers divisible by $2$ between $1$ and $100$. So, you might think there are $33 + 50 = 83$ numbers divisible by one or the other, but this is overcounting something. We're counting every number which is divisible by both $3$ and $2$ twice. So, for example, $6$ is counted once as a number divisible by $3$, and then again as a number divisible by $2$. So, we need to count how many numbers are divisible by both $3$ and $2$ and subtract this from what we had before. Being divisible by both $3$ and $2$ is the same thing as being divisible by $6$, so there are $16$ numbers between $1$ and $100$ divisible by both. Subtracting, there are $83 - 16 = 67$ numbers divisible by $3$ or $2$.